stress nd strain
TRANSCRIPT
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curve
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When some external forces are applied to abody . than the body oers internal resistanceto these force. the magnitude of the internalresistance force is numerically equal to theapplied force.
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stress=appliedload /area
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Tensile stressCompressive stress
Shear stress
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Tensile strain
Compressive strain
Shear strain
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tan=dl/l
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Methods of analysisMethods of analysis
(Load-stress load-deflection relations)
Method of mechanics ofmaterial
Method of continuum
mechanics & Elasticity
Energy methods
Equations of
equilibriumContinuity
condition
/ = E
Equilibrium equationfor elemental volume
Differential
compatibility equation
Generalized Hookeslaw
Also called scalar
method
!lane crosssection ofmember remainplane afterdeformation
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Stress-Strain RelationsStress-Strain Relations
Stress components must be relatedto the strain components.
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Material PropertiesMaterial Properties
! "odulus of#lasticity
! $oisson%s &atio! Shear "odulus
! $ercent#longation
'ield Strength
! (ltimate tensile
Strength! 'ield $oint
! "odulus of&esilience
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Engineering Stress and StrainEngineering Stress and Strain
0
P
LL L
e
=
= =
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!rue Stress and Strain!rue Stress and Strain
( )t
t
t
t
tt
t
L
t t
L
P
L L
dLd
L
Ld ln ln "
L
e
e
=
= +
=
+ = = = +
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Structural steel
ll dim# in mm
$$
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-20
-2
16
34
52
70
S
tre
ss
(k
s
i)
0 0.05 0.1 0.15 0.2 0.25 0.3Strain (in/in)
E%perimental Stress-Strain plot for "0" steel
Structural steel
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0 0.002 0.004 0.0060.008
Strain
0
125
250
375
500
Stress(!"
a)
#ra$ Cast %ron
Characteristic stress-
strain curve for brittle
materialCast Iron
0 0.06 0.12 0.180.24Strain
0
125
250
375
500
Stress(!"a)
2024-T351 &lu'inu' &llo$
Characteristic stress-strain curve for ductile
material
Aluminum
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Stress-strain curve for compression
Cast Iron
Copper
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Poissons ratio
Poisson's ratio can e determined indirectly from
stress-strain cure y *no+ing the change in the
cross-sectional area of the specimen at a point
along the elastic region of the stress-strain cure#
lateral strain
= -
axial strain
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"he !oisson ratio for most metals falls between#$% to #&%
'ubber has a !oisson ratio close to #% and istherefore almost incompressible(
Cork has a !oisson ratio close to zero )"his
makes cork function well as a bottle stopper* sincean a+ially,loaded cork will not swell laterally toresist bottle insertion-
"he !oisson.s ratio is bounded by two theoretical
limits/ it must be 0reater than ,1* and less than orequal to #%*
)2t is rare to encounter en0ineerin0 materials withne0ative !oisson ratios-
Some interesting points about Poissons ratio
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Failure and limits on design: (isotropicmaterial)
Stress based criteriaMaterial
TypeFailure Theories
Ductile 3a+imum shear stress criterion* von 3ises criterion
4rittle 3a+imum normal stress criterion* 3ohr.s theory
on-Stress based criteria
5tiffness* vibrational characteristics*fati0ue resistance* creep resistance
etc
,oulom-Mohr criteria
6or isotropic materials* only twoindependent elasticconstants areneeded for describin0 the stress,
strain relationship*
ie* Hooke.s 7aw ! = "
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or .uctile materialor .uctile material
or /rittle materialor /rittle material
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Common failure modes of a structural member:
"# ailure y e%cessie deflection"# ailure y e%cessie deflection
# ailure y general yielding# ailure y general yielding
1# ailure y fracture1# ailure y fracture
2# ailure y instaility (uc*ling)2# ailure y instaility (uc*ling)
"lastic deflection
#eflection by creep
Sudden $brittle% fracture
Fracture of crac&ed member
Progressive fracture' Fatigue